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Zbl 1221.34167
Li, Yongkun; Yang, Li
Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 14, No. 7, 3134-3140 (2009). ISSN 1007-5704

Summary: A class of Cohen-Grossberg neural networks with bounded and unbounded delays is considered. We establish some sufficient conditions on the existence and exponential stability of anti-periodic solutions for the following Cohen-Grossberg neural networks: $$ \multline x'_i(t)=-a_i(x_i(t))\Big[b_i(x_i(t))\\-\sum^n_{j=1}c_{ij}(t)f_j(x_j(t))- \sum^n_{j=1}d_{ij}(t)g_j(x_j(t-\tau_{ij}(t))) \\-\sum^n_{j=1}e_{ij}(t)\int^\infty_0k_{ij} (\theta)h_j(x_j(t-\theta))d\theta-I_i(t)\Big],\endmultline$$ $i=1,2,\dots,n.$ We also present an example to illustrate the feasibility and effectiveness of our results.

MSC 2000:: *34K05 General theory of functional-differential equations
34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology
92B20 General theory of neural networks

Keywords: Cohen; Grossberg neural networks (CGNNs); bounded and unbounded delays; anti-periodic solutions; exponential stability

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